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JDQZ method for the generalized eigenvalue problem

Posted: Tue Jul 28, 2015 4:50 am
by fletchjp
Are you looking at the JDQZ for MAGMA? This is a method for the solution of the generalised eigenvalue problem for a small no of eigenvalues.

It uses GMRES and optionally BiCGstab internally.

I was recommended to look at it and have only recently found the code at http://www.win.tue.nl/casa/research/sci ... tware.html

I have it working on my CPU for a small case (about 4000 square). It works quite well for up to 6 or 7 eigenvalues with a preconditioner of A-1 (via factorisation).

The results I get agree with Arpack for the same problem.

I have now been able to track down the following article here http://www.staff.science.uu.nl/~sleij101/JD_software/

References: D. R. Fokkema, G. L. G. Sleijpen, H. A. van der Vorst
Jacobi-Davidson style QR and QZ algorithms for the reduction of matrix pencils.
SIAM J. Sci. Comput., 20(1):94-125, 1998.

I hope this is of interest.

John

Re: JDQZ method for the generalized eigenvalue problem

Posted: Tue Jul 28, 2015 9:57 am
by hartwig anzt
Dear John,

thank you for pointing us to this! Generally, we would be very interested in having this - in particular for general eigenvalue problems. Unfortunately, we only do have very limited resources, so I can't promise we'll add this method within the next weeks.

What is the application you would need it for? An SPD problem? Did you try the LOBPCG eigensolver already available?

Thanks, Hartwig

Re: JDQZ method for the generalized eigenvalue problem

Posted: Tue Jul 28, 2015 12:29 pm
by fletchjp
Hartwig

Thank you for your response

I have been working with a colleague on large problems from fluid mechanics with dense matrices. We have successfully worked using Arpack and can use Magma to speed up the LAPACK calculations we need.

The JDQZ code uses a lot of LAPACK and BLAS, so a Magma version could be a matter of simply changing those calls. JDQZ also uses GMRES and BiCGstab internally.

I am only just starting with JDQZ and have so far only run a small case.

I am planning to have a look at your Magma implementation of GMRES/FGMRES. I can't do that yet as I have not yet sorted out my NVIDIA driver problem (see another thread) so can only run parts of Magma 1.6.2.

I don't know LOBPCG. I will look into it. I have found a few papers and it seems to be for symmetric problems and ours is not.

Thanks again

John